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Communications in Theoretical Physics

Photon blockade in a double-transmon system with ultrastrong coupling

Tian 甜 Tian 田, Xianhe 先和 Zhu 朱, Xi 茜 Tian 田

Published Sep 1, 2024• 0 citations
Publisher

Abstract

Abstract The circuit quantum electrodynamics (QED) system has brought us into an ultrastrong and deep coupling regime in the light–matter interaction community, in which the quantum effect has attracted significant interest. In this study, we theoretically investigated the photon blockade phenomenon in a double-transmon system operating in an ultrastrong coupling regime. We considered the effect of the counter-rotating wave terms in the interaction Hamiltonian and derived the master equation in the eigenpresentation. We found that photon blockade occurred in only one of the eigenmodes, and the counter-rotating wave terms enhanced the blockade by reducing the minimum value of the second-order correlation function. This study will be beneficial for the design of single-photon devices in circuit QED systems, especially in the ultrastrong coupling regime.

DOI
10.1088/1572-9494/ad75f3

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Abstract The circuit quantum electrodynamics (QED) system has brought us into an ultrastrong and deep coupling regime in the light–matter interaction community, in which the quantum effect has attracted significant interest. In this study, we theoretically investigated the photon blockade phenomenon in a double-transmon system operating in an ultrastrong coupling regime. We considered the effect of the counter-rotating wave terms in the interaction Hamiltonian and derived the master equation in the eigenpresentation. We found that photon blockade occurred in only one of the eigenmodes, and the counter-rotating wave terms enhanced the blockade by reducing the minimum value of the second-order correlation function. This study will be beneficial for the design of single-photon devices in circuit QED systems, especially in the ultrastrong coupling regime.
Abstract We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling, i.e. H i n t ∼ a ^ † 2 a ^ 2 ( b ^ 1 † + b ^ 1 ) . We find that the Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time second-order correlation function of the cavity photons and find that the optimal photon blockade does not happen at the single photon resonance. By working within the few-photon subspace, we get an approximate analytical expression for the correlation function and the condition for the optimal photon blockade. We also find that the photon blockade effect is not always enhanced as the Kerr-type nonlinear coupling strength g 2 increases. At some values of g 2 , the photon blockade is even weakened. For the system we considered here, the second-order correlation function can be smaller than 1 even in the unresolved sideband regime. By numerically simulating the master equation of the system, we also find that the thermal noise of the mechanical environment can enhance the photon blockade. We give out an explanation for this counter-intuitive phenomenon qualitatively.
We explore photon coincidence counting statistics in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime, usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis, we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counterrotating interaction terms.
In recent years, quantum Rabi model has aroused considerable interest because of its fundamental importance and potential applications in quantum technologies. For a conventional cavity-quantum-electrodynamic (cavity-QED) system involving the interaction between an atom and photons in a cavity, the atom-photon coupling frequency is much smaller than the transition frequency of the atom and the frequency of the cavity mode. This cavity-QED system is usually described by the Jaynes-Cummings model in which the rotating-wave approximation can be adopted by neglecting the counter-rotating coupling terms in the Hamiltonian of the system. However, by designing the unique structure of the superconducting circuit, the ultrastrong-coupling regime can be achieved in a circuit-QED system in which the counter-rotating coupling terms become as important as the rotating terms. Thus, the rotating-wave approximation cannot be used in the ultrastrongly coupled circuit-QED system. Owing to the ultrastrong coupling, this circuit-QED system is described by the standard quantum Rabi model when a superconducting qubit is coupled only to a single resonator mode. In this work, we experimentally study an ultrastrongly coupled circuit-QED system consisting of a four-junction superconducting flux qubit and a muti-mode coplanar-waveguide resonator. The transmission-spectrum measurement and numerical simulations show that the system is in the ultrastrong-coupling regime. By changing the photon number in the resonator, we observe the frequency shift of the flux qubit via the spectroscopic measurement. This frequency shift contains the contributions from not only the rotating-coupling terms but also the counter-rotating terms, which is in good agreement with the theory. The result indicates that this ultrastrongly-coupled quantum system can be used as a good platform to investigate the quantum Rabi model and has potential applications in various aspects of quantum technology, such as quantum simulation, ultrafast quantum gates, entangled-state preparation and protected qubits.
We investigate theoretically the performance of resonant two-qubit gates in the crossover from the strong to the ultrastrong coupling regime of light–matter interaction in circuit quantum electrodynamics. Two controlled-phase (CPHASE) gate schemes—which work well within the rotating wave-approximation—are analysed while taking into account the effects of counter-rotating terms appearing in the Hamiltonian. Our numerical results show that the fidelity of the gate operation is above 96% when the ratio between the coupling strength and the resonator frequency, g / ω r , is about 10%. Novel schemes are required in order to implement ultrafast quantum gates when increasing the ratio g / ω r .
Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.
Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation.